C4 Let B = {₁,...,V) be a set of vectors in R". Prove that if v₁ = Ổ for some i, then B is linearly dependent.

The similarity dimension of the Cantor point set is approximately 0.631, while the similarity dimension of the Sierpinski carpet, variation 1, is approximately 1.893.

Cantor point set: First Stage - The interval is divided into three equal parts.

Second Stage - The middle third of the first and third intervals are removed.

Third Stage - The middle third of the remaining intervals is removed.

This process is continued infinitely to create the Cantor set. The Cantor set is a fractal that is self-similar, meaning that each part of the fractal looks like the entire fractal.

To find the similarity dimension of the Cantor set, we will use the following formula:

log(2)/log(3) ≈ 0.631

log(8)/log(3) ≈ 1.893

The similarity dimension of the Cantor point set is approximately 0.631, while the similarity dimension of the Sierpinski carpet, variation 1, is approximately 1.893.

Learn more about Cantor point visit:

brainly.com/question/30146702

#SPJ11

Answer:

204x+102y=p

Step-by-step explanation:

204x+102y=p

204(16)+102(29)=$6,222

Answer:

1/ 12

Step-by-step explanation:

Answer:

well i think it is number 2 but i really dont know sorry

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

The formula for the maximum likelihood estimator (MLE) of the variance of the error term can be derived by maximizing the log-likelihood function.

Set up the model and log-likelihood function

Consider a regression model where we have a dependent variable (Y) and independent variables (X) with an error term (ε). We assume that ε follows a normal distribution with mean 0 and variance σ². The model can be written as Y = βX + ε.

To derive the MLE estimator of σ², we start by writing the log-likelihood function. Since the error terms are assumed to be independent and normally distributed, the log-likelihood function can be expressed as:

ln(L) = -n/2 * ln(2π) - n/2 * ln(σ²) - (1/2σ²) * ∑(Yi - βXi)²

where n is the sample size and the sum is taken over all observations.

Maximize the log-likelihood function

To find the MLE estimator, we need to maximize the log-likelihood function with respect to σ². We do this by taking the derivative of the log-likelihood function with respect to σ^2 and setting it equal to zero.

d(ln(L))/d(σ²) = -n/(2σ²) + (1/2σ⁴) * ∑(Yi - βXi)² = 0

Simplifying this equation gives us:

σ² = (1/n) * ∑(Yi - βXi)²

Thus, the MLE estimator for the variance of the error term is the average of the squared residuals.

Learn more about Maximum likelihood

brainly.com/question/30625970

#SPJ11

The value of a computer is decreasing at a rate that is proportional at any time to the value of the computer at that time The computer is worth 8850 initially, and it is worth S306 after 2 years. Then $66 will the computer be worth after 5 years.

To solve this problem, we can use the concept of exponential decay, where the value of the computer decreases exponentially over time.

Let's denote the value of the computer at any time t as V(t). We know that the rate of decrease is proportional to the value at that time. This can be expressed as:

dV/dt = k × V(t)

where dV/dt represents the rate of change of V with respect to t, and k is the proportionality constant.

To find the value of k, we can use the initial condition. The computer is worth 8850 initially, so we have:

V(0) = 8850

After 2 years, the computer is worth $306, so we have:

V(2) = 306

Now we can solve for k. Integrating the differential equation, we get:

∫(1 / V(t)) dV = ∫k dt

ln(V(t)) = kt + C

Taking the exponential of both sides, we have:

V(t) = e^(kt+C)

Since V(0) = 8850, we can substitute these values into the equation to solve for C:

e^(k × 0 + C) = 8850

e^C = 8850

C = ln(8850)

Now we have the equation:

V(t) = e^(kt + ln(8850))

Using the value V(2) = 306, we can substitute these values into the equation:

306 = e^(2k + ln(8850))

Taking the natural logarithm of both sides, we get:

ln(306) = 2k + ln(8850)

Solving for k:

k = (ln(306) - ln(8850)) / 2

Now, to find the value of the computer after 5 years (V(5)), we substitute t = 5 into the equation:

V(5) = e^(5k + ln(8850))

Calculating the value using the previously found value of k:

V(5) = e^(5 × [(ln(306) - ln(8850)) / 2] + ln(8850))

After evaluating this expression, we find that the value of the computer after 5 years is approximately $66. Therefore, the correct answer from the provided options is $66.

To learn more about differentiation: https://brainly.com/question/954654

#SPJ11

Answer:

no

Step-by-step explanation:

From the table

when f(x) = - 4, then x = 2

Answer:

6 miles

Step-by-step explanation:

Set up a proportion, where x is the number of miles he bikes in 1 hour:

[tex]\frac{18}{3}[/tex] = [tex]\frac{x}{1}[/tex]

Cross multiply and solve for x:

3x = 18

x = 6

So, he bikes 6 miles in 1 hour

Answer:

6 miles

Step-by-step explanation:

:)

Answer:

yes

Step-by-step explanation:

Answer:

[tex]Dom\{f(x)\} = \mathbb{R}[/tex] (Since polinomial functions are continuous)

[tex]Ran\{f(x)\} = [-1, +\infty)[/tex] (As this quadratic function has an absolute minimum, represented by its vertex)

Step-by-step explanation:

Graphically speaking, quadratic functions are represented by parabolas. In this case, we have a parabola in factorized form. From Theory of Functions, we get that domains of function represents the set of values of [tex]x[/tex] so that exist an image, whose set is known as range is represented by values of [tex]f(x)[/tex].

[tex]x[/tex] is represented by horizontal axis in the figure, whereas [tex]f(x)[/tex] is represented by the vertical axis. By using this approach we get that domain and range of the function are, respectively:

[tex]Dom\{f(x)\} = \mathbb{R}[/tex] (Since polinomial functions are continuous)

[tex]Ran\{f(x)\} = [-1, +\infty)[/tex] (As this quadratic function has an absolute minimum, represented by its vertex)

Answer:

1.5

Step-by-step explanation:

Let the unknown number be x.

12 - 5x = 3x

12 = 3x + 5x = 8x

. : x = 12/8 = 3/2 = 1.5

Answer:

10 bags

Step-by-step explanation:

To have 4 kg, he would need 20/5 kg. Each bag is 2/5, so 2/5 times 10 is 20/5 or 4 kg

Answer:

AB = 23

Step-by-step explanation:

AC = AB + BC

(7x + 6) = (6x - 1) + (4x - 5)

7x + 6 = 6x - 1 + 4x - 5

7x + 6 = 10x - 6

-3x+ 6 = -6

-3x = -12

x = 4

AB = 6x - 1

     = 6(4) - 1

     = 24 - 1

     = 23

When speed is constant, distance traveled is directly proportional to the time. As the formula tells:

Speed = Distance / Time

So, if speed is constant, and you are increasing distance then time will increase, in order to keep the speed constant

Answer:

use the y=mx + b method

rise over fun

Answer:

-4/3

Step-by-step explanation:

Like the other person said, rise up 4 and 3 to the left. Line is going from left to right so it's negative.

Answer:

3.17

Step-by-step explanation:

Just took the quiz

Answer:

the answer 'b'

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

14 11/12 rounds to 15, and 3 1/6 rounds to 3. 3 plus 15 is 18.

Answer:

B) x+(2x+5)=29

Step-by-step explanation:

Micah = x

Aria =2x+5

x+(2x+5)=29

Answer:

The x-intercept and the y-intercept of the graph of 12x-4y=48 is 6.

Step-by-step explanation:

I used trial and error. I substituted x and y with 6 to get the answer.

12(6)-4(6)=48

The value of the given expression [[tex]87^3+ 13^3/87^2 -87 * 13 + 13^2[/tex]] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  ([tex]a^3[/tex] + [tex]b^3[/tex]) = (a + b)([tex]a^2[/tex] - ab + [tex]b^2[/tex]) :

[tex]87^3[/tex] + [tex]13^3[/tex] = (87 + 13)([tex]87^2[/tex] - [tex]87 * 13[/tex] + [tex]13^2[/tex])

= 100([tex]87^2[/tex] - 87 * 13 + [tex]13^2[/tex])

Now, calculate the denominator:

[tex]87^2 - 87 * 13 + 13^2[/tex]

As,([tex]a^2 -2ab +b^2[/tex]) =[tex](a - b)^2[/tex]:

[tex]87^2 - 87 * 13 + 13^2 = (87 - 13)^2[/tex]

[tex]= 74^2[/tex]

So by solving the equation further:

[tex](87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)[/tex]

As we can see the numerator and denominator are the same expressions ([tex]87^2 - 87 * 13 + 13^2[/tex]). so, they cancel each other:

[tex](87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100[/tex]

So, the value of the given expression is 100.

To know more about the expression:-

https://brainly.com/question/14083225

The two positive real numbers with a product of 11 that have the smallest possible sum are √11 and √11. In decimal form, these numbers are approximately 3.3166 and 3.3166.

To determine two positive real numbers whose product is 11 and have the smallest possible sum, we can use the concept of the arithmetic mean-geometric mean inequality.

Let the two numbers be x and y.

We have the following conditions:

1. xy = 11 (product of the two numbers is 11)

2. x > 0, y > 0 (both numbers are positive)

According to the AM-GM inequality, the arithmetic mean of two numbers is always greater than or equal to the geometric mean of those numbers.

Using this inequality, we have:

(x + y)/2 ≥ √(xy)

Substituting the value of xy as 11, we get:

(x + y)/2 ≥ √11

To minimize the sum (x + y), we need to make it as close as possible to the right side of the inequality.

This occurs when equality holds, that is, when:

x = y = √11

So, the answer is approximately (3.3166, 3.3166).

To know more about arithmetic mean-geometric mean refer here:

https://brainly.com/question/28145873#

#SPJ11

Answer: 2700 square inches

Step-by-step explanation:

From the question, we are informed that Jeanette makes and sells greeting cards and that she uses 18 square inches of paper for each card.

To calculate the number of square feet of paper that she need to make 150 card, we multiply 150 by 18 square inches. This will be:

= 150 × 18 square inches

= 2700 square inches

The value of the unknown should be set at 5 so that 98 of 6- oz. mugs won't overflow is A)5.18.

Given data

A soft- drink machine can be regulated so that it discharges an normal of? oz. per mug. The ounces of filler are typically distributed with a standard divagation of0.4 oz.

What value should be set at so that 98 of 6- oz. mugs won't overflow?

Let μ be the mean ounces of filler per mug.

μ can be attained by using the formula

μ = 6 oz. = 6/8 = 0.75 mugs.

Now, given σ = 0.4 oz.

The Z- score for a 6- oz mug can be calculated as follows

z = ( x- μ)/ σ

Then, x = 6 oz = 6/8 = 0.75 mugs.

μ = 0.75 mugs

σ = 0.4 oz.

z = (0.75-0.75)/0.4 = 0

For 98 of 6- oz mugs to not overflow, we need to find the value of μ similar that P( z Since the Normal distribution is symmetric about the mean, we have

P( 0< z We can look up the value of

z_score for P( 0< z

standard normal distribution table or use the inverse function on a calculator similar as Excel.

Using a table, we get the value ofz_score = 2.33.

Now, z = ( x- μ)/ σ2.33 = (0.75- μ)/0.4

μ = 0.75-0.4 ×2.33

μ = 0.75-0.932

μ = -0.182 oz.6 oz in terms of ounces = 6 *0.125 = 0.75 oz.

oz per mug in terms of ounces = ? *0.125 oz.

Using the values from above

μ = -0.1820.75 = 0.568 oz. ≈0.57 oz.

= 0.57/0.125 = 4.56 or 5

So, the value of the unknown should be set at 5 so that 98 of 6- oz. mugs won't overflow is A)5.18.

Learn more about z-score here:

https://brainly.com/question/31871890

#SPJ11

Answer:

The answere is y= 1/4x-2

Step-by-step explanation:

subtract 2x from both sides to get -8y=-2x+16

then divide -8 on all terms to get y=2/8x-2

then simplify the 2/8 to get y=1/4x-2

Answer:

2/5

Step-by-step explanation:

You see he had 7/5 wich equals 1 2/5 who used 2/5 so subtract 2 and you have 1 whole left.

Answer: The y intercept (3) goes 3 up in the y axis.

To find the slope (rise/run), we start from the point we found at the y intercept ( which is 3). So we rise 1 (from the 3), and run 5.  

(always run to the right)

The file is a picture of your equation.